Am 11.01.2012 04:32, schrieb Chris Smith:
On Wed, Jan 11, 2012 at 4:43 AM, Joachim Durchholz<[email protected]> wrote:
f/g will be x, which is continuous. So yes, in this case, the
simplification changes the result.
Since x**2/x is automatically simplified, we should probably automatically
simplify x**2.0/x.
x²/x has a discontinuity for x=0, and x does not, hence x²/x is not the
same as x. (I suspect it might even be possible to "prove" 1=0 if you
allow removing 0/0 from a product. Division by zero tends to be nasty
like that, but I haven't checked.)
However, (if x = 0 then 0 else x²/x) is the extension by continuity of
x²/x, and is indeed equal to x.
So:
Simplifying (x**2/x if x != 0 else 0) and (x**2/x if x != 0 else x) to x
is valid.
Simplifying extend_by_continuity(x**2/x) to x is valid (assuming a
hypothetical function extend_by_continuity).
simplify(x**2/x, extend_by_continuity=true) could be defined to return a
simplified expression that may, at the discretion of simplify(), have
been extended by continuity.
But simplifying x**2 to x in the general case is invalid.
If simplify does that without being told to do that, that's a bug.
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